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The Gills came agonisingly close to scoring a late winner against Oldham.
Mark Byrne made a superb goalline clearance to deny Oldham’s Queensy Menig in the second half.
But Gillingham came even closer with Luke O’Neill’s stoppage time free-kick that was turned onto the bar by keeper Johny Placide.
The result means the Gills still only have one home league win this season but their unbeaten run now stands at seven games in all competitions.
Manager Steve Lovell, who named an unchanged starting XI, was looking to clinch a first home league win, taking two points from his three in charge so far at Priestfield.
That form was in contrast to their impressive away results under Lovell, which stands at three wins and a draw from the four so far.
The game was only 12 minutes old when Lee Martin received a blow from a clearance that left his sparked out. He was eventually stretchered off after receiving lengthy treatment.
Prior to that Josh Parker had a shot deflected wide for the Gills while Tomas Holy made a save to deny Craig Davies.
Once play resumed, with 20 minutes on the clock, the Gills switched to a flat back four, having started the game with wing-backs.
Oldham’s top scorer Eoin Doyle was denied by a super Gabriel Zakuani tackle and the striker also had a shot saved one handed by Holy, who did well to reacts as the ball moved wickedly mid-flight.
Gillingham had few clear-cut chances but were unlucky not to have been awarded a penalty when Wilkinson raced into the box and was felled. Referee Graham Horwood had only just turned down a penalty shout from Oldham’s Jack Byrne and squared it up by saying no to the Gills too.
Oldham made a lively start to the second half and Doyle’s cross was nearly put into his own net by Connor Ogilvie, the defender glad to see the ball trickle just wide.
Byrne had a shot saved for the Gills and Holy was kept busy at the other end, saving well after Doyle raced onto a ball that had been threaded through by Dan Gardner.
Davies’ free-kick came close to breaking the deadlock, after Byrne had committed a foul on the edge of Gills’ box, but Holy did well to get down and save the shot.
Eaves fired an effort wide for the Gills and Jake Hessenthaler did likewise from further out. Josh Parker had a better chance than both, after beating defender Kean Bryan, only to fire the shot well over.
Gills’ good spell came to an abrupt end when sub Queensy Menig took on the defence, beat keeper Holy, only to see his goalbound effort poked off the line by Mark Byrne. Former Ajax man Menig put another chance over the bar soon after.
Wilkinson headed wide for the Gills when well positioned while Doyle hit a weak shot at Holy and then put another over as the visitors broke from a corner.
Gillingham had the chance to score a stoppage-time winner but O’Neill’s shot was tipped onto the frame of the goal, rolling out for a corner kick which was cleared.
Gillingham: Holy, Zakuani, O’Neill, Ogilvie, Hessenthaler, Byrne, Martin (Wagstaff 20mins), Clare, Parker (List 81mins), Eaves, Wilkinson. Subs not used: Arnold, Nugent, Ehmer, Chapman, Cundle.
Oldham: Placide, Dummigan, Gerrard, Gardner (Green 68mins), Davies (Holloway 59mins), Doyle, Hunt, Fane, Nepomuceno (Menig 64mins), Byrne, Bryan. Subs not used: Ben Wilson, Brian Wilson, Clarke, Obadeyi.
Attendance: 4,364 (229 away)